Planning problems, particularly for robotic manipulation tasks, may
often be cast as discrete graph search problems. Motions in the graph
are generally nondeterministic or stochastic as a result of control
and sensing errors in the underlying physical system. The global
capabilities of such a system may be modeled by the homotopy type of a
"strategy complex". The simplices of this complex may be viewed as
the eventually-convergent control laws (aka plans or strategies)
possible on the graph.

One result that appears via this perspective is a controllability
theorem: The robot can move anywhere in its state graph despite
control uncertainty (adversarial or stochastic) precisely when the
graph's strategy complex is homotopic to a sphere of dimension two
less than the number of states. This talk discusses that and related
results.

Biography

Michael Erdmann is a Professor of Computer Science and Robotics at
Carnegie Mellon University. He obtained his PhD in 1989 from MIT
under the supervision of Tomas Lozano-Perez, received an NSF
Presidential Young Investigator Award in 1991, and is a Fellow of the
IEEE. He was a Technical Editor of the IEEE Transactions on Robotics
and Automation and is currently on the Editorial Board of the
International Journal of Robotics Research. His recent research has
focused on applying topological methods to engineering problems,
including modeling protein structure, planning with uncertainty, and
understanding privacy.